Blow Up Of Solutions To Wave Equation With Linear, Nonlinear Damping And Source Terms

In this paper,By use of two different methods,we consider the non-existence of theglobal solution to the cauchy problem of the k-laplacian non-linear wave equation withdamping and source terms in Rⁿ(n≥2)where k≥2,p≥1,m≥1 It is verified that,when the initial energy E(0)<0,thesolution to the problem is bound to blow up in finite time for linear damping equationand u₀(x)∈W^1,k(Rⁿ),u₁(x)∈L²(Rⁿ) with compact support,when the initial energyE(0)